The concentration C of phenylbutazone in micrograms per mili

The concentration, C, of phenylbutazone, in micrograms per milimeter (ug/ML), in the plasnma of a calf injected with this anti-inflammatory agent is given approximately by

C(t) = 42.03e^-0.01050t

where t is the number of hours after the injection and 0 ? t ? 120

Refer to graph

a) Given that this model is accurate for 0 ? t ? 120, what is the initial dosage?

b) What is the average amount of phenylbutazone in the calf\'s body for the time between 10 and 120 hours?

Solution

a) Given that this model is accurate for 0 t 120, what is the initial dosage?

intial dosage means at time t = 0

we have

C(t) = 42.03e^-0.01050t

at t= 0

C(0) = 42.03 ug/ml injected

b) What is the average amount of phenylbutazone in the calf\'s body for the time between 10 and 120 hours?

between 10 and 120 hours

C(10<t<120) = C(10) - C(120)

                   = 42.03e^[-0.01050*10] - 42.03e^[-0.01050*120]

                  = 37.8406397 - 11.9219787

                  = 25.92ug/ml